Well first off, about the tuner, picks, and all of that. A lot of bassists prefer to use their fingers, so you don't actually NEED any picks. They will give you a different sound though. Fortunately, Guitar Center usually has a couple picks lying around. You can usually find them atop of amps in the guitar section, or just ask an employee. You can take a couple without anyone caring.
And you should buy a tuner. There's a ton of methods for tuning a bass, and don't forget, the Internet can be a great resource, but an actual tuner is a good idea. As for metronomes, you can find various free ones online, like this one:
http://www.metronomeonline.com/
Now to convince your parents... see, every bass has a different feel to it. Some people like one type of neck, while others like another. For example, I have small hands, so I originally only tried out basses with thin necks. I eventually decided on an Ibanez SRX300, which has a very thin neck. However, after my playing developed, I realized that the thin neck was very uncomfortable for me, and I wanted a bigger neck. I went to Guitar Center and played a Warwick, and it's baseball bat-like neck did it for me. Since I started playing Warwicks, my fretting hand feels less fatigued; I can also play smoother, faster, and cleaner. So feeling the bass is very important. I mean, I love the huge Warwick neck, but there's tons of people on this site alone that probably can't stand it. It's all preference.
Also, Squiers aren't that bad. In my opinion, most sound a little boring... but some are excellent for the price. This is another reason why you need to get out there and play as many basses as possible -- tell your parents that with cheaper companies like Squier, the quality can vary from model to model, even if they seem like the exact same bass.
Personally though, I think Ibanez is the way to go if you want a cheap, new bass.
As for buying used... most music stores will let you try out any used gear they have to my knowledge, so just pick it up and play it like you would any other guitar. Don't forget, an instrument is as big of an investment for you as it is for the person next to you; chances are they took good care of their gear, and they damn well should if they expect to sell it on later in it's life.
Edit: Just realized I posted in a thread that was ollllld. Oh well.